Here's where it gets fun. The more cream cheese you use, the denser the cheesecake will be (but not dry!) The more eggs you use, the fluffier it will be. There's a delicate balance here - 1 lb cheese and 3 eggs will give you a fluffy cheesecake, but if you use 2 lbs cheese, 3 eggs is an absolute must if you don't want it to be flat. More eggs than 3, and you'll taste the eggs. 1 lb cheese and 2 eggs is a nice balance, too, but going any lower than that you'll just end up with something flat.
The powdered sugar works best for two reasons - number one, powdered sugar contains corn starch, which acts as a thickener, and number two, you don't have to worry about the grittiness of undissolved sugar in your cake. The yogurt or sour cream adds moistness and a little bit of tang to the cake. It's not necessary, but it adds oomph to either a bland cake or a citrus-flavored cake. For liqueur, add no more than ½ cup if you're using the yogurt or sour cream, and make sure you're using the three eggs. If you eliminate the yogurt/sour cream, you can increase the liqueur to ¾ cup, and 2 eggs will work (but three is still better - two works best only if you're not using the yogurt/sour cream >and< your liqueur is only ½ cup.) A fruit or vegetable puree should be relatively dry - drain off the liquid in a sieve, or put it in a saucepan, mix in some cornstarch, and heat it until it's thick. You can use an entire cup of puree if you eliminate the yogurt/sour cream. Either mix in the puree with the batter, or reserve a cup or so of batter, mix it with the puree, then swirl it into the cheesecake.
The vanilla is a must, in my opinion. Lots of times, I'll throw in an extra teaspoon for good measure. Other extracts can enhance the flavor - banana extract in a strawberry cheesecake, coconut extract or almond extract in an Amaretto cheesecake, etc.
Another addition would be cocoa or chocolate. Cocoa mixes in nicely without making the cheesecake gooey - 4-6 Tbsp will do it. Melted chocolate or white chocolate chips shouldn't really exceed 6 oz, even 4 oz will usually do enough for the flavor. If you're doing the swirl thing, use only 2-3 oz melted chocolate for the batter that's being swirled in. Make sure the melted stuff is cooled before you mix it in.
(see also Basic Cheesecake Crust and Basic Cheesecake Method & Toppings)
Your Basic Cheesecake Filling is ready. Bon appetit!
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